7-speed Shimano indexing will not work with an old Suntour freewheel. Since you're not happy with your Shimano freewheel, I think your best bet is to get a new cassette wheel spaced for 8/9/10-speed. Make sure you know the spacing of the rear triangle before purchase, it's probably 130mm, which is considered road spacing now. A lot of hubs will have mtb/touring spacing of 135, so watch for that. You'll need a new shifter to match the cassette, too. That LX derailleur will handle 8- or 9-speed cassette/shifters, and there's tons of gearing options for them.